[Computational Complexity] What is the least boring number (NOT the usual par...
- What is the first boring natural number? I am NOT going to present that the first boring natural number is interesting crap, which may qualify as the most boring paradox.
The question is, of course, ill defined. I will define it a little better by only considering mathematical properties of numbers. (e.g., 7 is interesting because there are 7 days of the week will not work.)Here are my opinions, and my opinions of my opinions. I will write WEAK if I think the justification for calling that number interesting is weak. In those cases if you know a better one, then comment on it.
- 1 is interesting as it is the multplicative identity.
- 2 is interesting because it is the only even prime. Also the first prime.
- 3 is interesting because it is the first odd prime. Also the first Mersenne prime.
- 4 is interesting because it is the first non-trivial square. Also it is the first number that is the sum of two primes.
- 5 is interesting because it is the first number that is the sum of two distinct squares and the first number that is the sum of two distinct primes. (WEAK)
- 6 is the first perfect number (though there are so few perfect numbers that ALL of them are interesting.)
- 7 is the first number such that the number of squares needed to add up to it is 4 (All numbers are the sum of 4 or less squares. There are an infinite number of numbers that require 4 squares: all of the numbers congruent to 7 mod 8.)
- 8 is the first non-trivial cube.
- 9 is the first non-trivial odd square. (weak)
- 10 is the first number that is the sum of two distinct odd squares. First triangular number that is the sum of 3 squares. (weak)
Posted By GASARCH to Computational Complexity at 8/18/2009 09:05:00 AM